This paper proposes ST-Raptor, a novel framework for automating query answering of semi-structured tables, widely used in real-world applications. Semi-structured tables have complex layouts, such as hierarchical headers and merged cells, making accurate query answering difficult using existing NL2SQL, NL2Code, and multi-modal LLM QA methods. ST-Raptor uses hierarchical orthogonal trees (HO-trees) to represent complex layouts and enables LLM query processing through basic tree operations. It decomposes user queries into subqueries, generates a tree operation pipeline, and performs operation-table alignment to ensure accurate pipeline execution. Furthermore, forward and backward validation are used to enhance the accuracy of the results. We evaluate the performance of our approach using a new dataset, SSTQA, consisting of 102 real semi-structured tables and 764 questions, achieving up to 20% higher accuracy than existing methods.